Can we invoke a servlet from a Java class.

Learn about it here

Check "Applet To Servlet Communication" blog entry(second entry from this one) to find out how to use

java.net.URL
java.net.URLConnection, classes.

Can we execute a servlet from command prompt?

We can't run a servlet as a standalone java application from the command line, we can use a browser to invoke a servlet if it's running in a container.